What is the slant height for the given pyramid to the nearest whole link?
Pyramid base: 10 cm
Height: 12 cm
A. 7 cm
B. 11 cm
C. 13 cm
D. 16 cm
AAAaannndd the bot gets it wrong yet again!
Draw a side view, and it should be clear that
(10/2)^2 +12^2 = s^2
s = 13
To find the slant height of a pyramid, we can use the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
In this case, the other two sides are the height (12 cm) and half the length of the base (10/2 = 5 cm).
So, we have:
Slant height^2 = height^2 + (half the base)^2
Slant height^2 = 12^2 + 5^2
Slant height^2 = 144 + 25
Slant height^2 = 169
To find the slant height, we take the square root of both sides:
Slant height = √169
Slant height = 13
Therefore, the slant height of the given pyramid is approximately 13 cm, which is option C.
To find the slant height of a pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height of the pyramid and the distance from the apex (top) to a point on the base.
In this case, we have the height of the pyramid (12 cm) and the length of the base (10 cm), which form a right triangle.
To find the length of the slant height (hypotenuse), we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, the slant height, h, can be found using the formula:
h^2 = 10^2 + 12^2
Simplifying:
h^2 = 100 + 144
= 244
To find the slant height, we take the square root of both sides:
h = √244
Using a calculator, we get:
h ≈ 15.62 cm
Rounded to the nearest whole link, the slant height is approximately 16 cm.
Therefore, the correct answer is D. 16 cm.